F(x) = ax 2 + bx + c. Jika F(1) = -4, F(0) = -3 dan F(-1) = 10. Tentukan F(x)

F(x) = ax 2 + bx + c. Jika F(1) = -4, F(0) = -3 dan F(-1) = 10. Tentukan F(x)

Jawab:

$f(x) = -x^{2} - 3$

Penjelasan dengan langkah-langkah:

f(x) = a $x^{2}$ + bx + c

f(1) = a + b + c = -4…(1)

f(0) = c = -3

f(-1) = a – b + c = 10…(2)

Substitusi c = -3

a + b – 3 = -4…(1)

a + b = -1

a – b – 3 = -4…(2)

a – b = -1

Eliminasi persamaan (1) dan (2)

a + b = -1

a – b = -1

———— –

2b = 0

b = 0

a – 0 = -1

a = -1

Diketahui a = -1, b = 0, dan c = -3

Maka f(x) = $-x^{2}$ – 3